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1Definitions

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1.1Synonyms and near-synonyms for the term classification

1.2Basic units

2Methods of classification

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2.1Logical and rationalist approaches

2.2Empiricist approaches

2.3Historical and hermeneutical approaches

2.4Pragmatic, functionalist and teleological approaches

3Examples of important classification systems

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3.1Periodic table

3.2Linnaean taxonomy

3.3Astronomy

3.4Hornbostel–Sachs classification of musical instruments

3.5Diagnostic and Statistical Manual of Mental Disorders (DSM)

4Philosophical issues

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4.1Artificial versus natural classification

4.2Taxonomic monism vs. pluralism

5List of classification systems

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5.1Business, organizations, and economics

5.2Mathematics

5.3Media

5.4Science

5.5Other

6Organizations involved in classification

7See also

8References

9External links

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Classification

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From Wikipedia, the free encyclopedia

Classification theory

This article is written like a research paper or scientific journal. Please help improve the article by rewriting it in encyclopedic style and simplify overly technical phrases. (October 2023) (Learn how and when to remove this template message)

Classification is a broad concept that comprises the process of classifying, the set of groups resulting from classifying, and the assignment of elements to pre-established groups. Classifying is a fundamental concept and a part of almost all kinds of activities. Classification itself is an interdisciplinary field of study, with contributing disciplines including philosophy, biology, knowledge organization, psychology, statistics, and mathematics.

Definitions[edit]

The term classification can apply to one or all of:

the process of classifying (distinguishing and distributing kinds of entities into different groups)[1]

a resulting set of groups, known as classes[2] (also called a classification system)

the assignment of elements to pre-established classes

Classifying—in the broad meaning given above—is a fundamental concept and a part of almost all kinds of activities.

Frederick Suppe[3] distinguished two senses of classification: a broad meaning, which he called "conceptual classification" and a narrow meaning, which he called "systematic classification".

About conceptual classification Suppe wrote:[3]: 292 "Classification is intrinsic to the use of language, hence to most if not all communication. Whenever we use nominative phrases we are classifying the designated subject as being importantly similar to other entities bearing the same designation; that is, we classify them together. Similarly the use of predicative phrases classifies actions or properties as being of a particular kind. We call this conceptual classification, since it refers to the classification involved in conceptualizing our experiences and surroundings"

About systematic classification Suppe wrote:[3]: 292 "A second, narrower sense of classification is the systematic classification involved in the design and utilization of taxonomic schemes such as the biological classification of animals and plants by genus and species.

Synonyms and near-synonyms for the term classification[edit]

One or more of the following terms are by some authors considered synonyms for classification while other authors have suggested various ways of differentiating these terms.

Concept/conceptualization

Categorization is, for example, mostly used by cognitive psychologists for what other call classification. Much of the contents of the Wikipedia article categorization is equally true for classification

Ordering

Taxonomy was first used in biology, but the term has spread to other domains. There may only be historical reasons that, for example, the periodic table is called a classification rather than a taxonomy

Typology

Division (e.g., logical division)

Basic units[edit]

Hull (1998) suggested "The fundamental elements of any classification are its theoretical commitments, basic units and the criteria for ordering these basic units into a classification".[4]

The basic units in a classification system are classes.

There is a widespread opinion in knowledge organization and related fields that such classes corresponds to concepts. We can, for example, classify "waterfowls" into the classes "ducks", "geese", and "swans"; we can also say, however, that the concept “waterfowl” is a generic broader term in relation to the concepts "ducks", "geese", and "swans". This example demonstrates the close relationship between classification theory and concept theory. A main opponent of concepts as units is Barry Smith.[5] Arp, Smith and Spear (2015) discuss ontologies and criticize the conceptualist understanding.[6]: 5ff The book writes (7): “The code assigned to France, for example, is ISO 3166 – 2:FR and the code is assigned to France itself — to the country that is otherwise referred to as Frankreich or Ranska. It is not assigned to the concept of France (whatever that might be).” Smith's alternative to concepts as units is based on a realist orientation, when scientists make successful claims about the types of entities that exist in reality, they are referring to objectively existing entities which realist philosophers call universals or natural kinds. Smith's main argument - with which many followers of the concept theory agree - seems to be that classes cannot be determined by introspective methods, but must be based on scientific and scholarly research. Whether units are called concepts or universals, the problem is to decide when a thing (say a "blackbird") should be considered a natural class. In the case of blackbirds, for example, recent DNA analysis have reconsidered the concept (or universal) "blackbird" and found that what was formerly considered one species (with subspecies) are in reality many different species, which just have chosen similar characteristics to adopt to their ecological niches.[7]: 141

An important argument for considering concepts the basis of classification is that concepts are subject to change and that they changes when scientific revolutions occur. Our concepts of many birds, for example, have changed with recent development in DNA analysis and the influence of the cladistic paradigm - and have demanded new classifications. Smith's example of France demands an explanation. First, France is not a general concept, but an individual concept. Next, the legal definition of France is determined by the conventions that France has made with other countries. It is still a concept, however, as Leclercq (1978) demonstrates with the corresponding concept Europe.[8]

Hull (1998) continued:[4] "Two fundamentally different sorts of classification are those that reflect structural organization and those that are systematically related to historical development." What is referred to is that in biological classification the anatomical traits of organisms is one kind of classification, the classification in relation to the evolution of species is another (in the section below, we expand these two fundamental sorts of classification to four). Hull adds that in biological classification, evolution supplies the theoretical orientation.[4]

Methods of classification[edit]

Classification itself is an interdisciplinary field of study. Important contributing disciplines include philosophy, biology, knowledge organization, psychology, statistics and mathematics.

Ereshefsky (2000) presented and discussed three general philosophical schools of classification: "essentialism, cluster analysis, and historical classification. Essentialism sorts entities according to causal relations rather than their intrinsic qualitative features."[9]

These three categories may, however, be considered parts of broader philosophies. Four main approaches to classification may be distinguished: (1) logical and rationalist approaches including "essentialism"; (2) empiricist approaches including cluster analysis (It is important to notice that empiricism is not the same as empirical study, but a certain ideal of doing empirical studies. With the exception of the logical approaches they all are based on empirical studies, but are basing their studies on different philosophical principles). (3) Historical and hermeneutical approaches including Ereshefsky's "historical classification" and (4) Pragmatic, functionalist and teleological approaches (not covered by Ereshefsky). In addition there are combined approaches (e.g., the so-called evolutionary taxonomy", which mixes historical and empiricist principles).

Logical and rationalist approaches[edit]

Logical division[10] (top-down classification or downward classification) is an approach that divides a class into subclasses and then divide subclasses into their subclasses, and so on, which finally forms a tree of classes. The root of the tree is the original class, and the leaves of the tree are the final classes. Plato advocated a method based on dichotomy, which was rejected by Aristotle and replaced by the method of definitions based on genus, species, and specific difference.[11] The method of facet analysis (cf., faceted classification) is primarily based on logical division.[12] This approach tends to classify according to "essential" characteristics, a widely discussed and criticized concept (cf., essentialism). These methods may overall be related to the rationalist theory of knowledge.

Empiricist approaches[edit]

"Empiricism alone is not enough: a healthy advance in taxonomy depends on a sound theoretical foundation"[13]: 548

Phenetics or numerical taxonomy[14] is by contrast bottom-up classification, where the starting point is a set of items or individuals, which are classified by putting those with shared characteristics as members of a narrow class and proceeding upward. Numerical taxonomy is an approach based solely on observable, measurable similarities and differences of the things to be classified. Classification is based on overall similarity: The elements that are most alike in most attributes are classified together. But it is based on statistics, and therefore does not fulfill the criteria of logical division (e.g. to produce classes, that are mutually exclusive and jointly coextensive with the class they divide). Some people will argue that this is not classification/taxonomy at all, but such an argument must consider the definitions of classification (see above). These methods may overall be related to the empiricist theory of knowledge.

Historical and hermeneutical approaches[edit]

Genealogical classification is classification of items according to their common heritage. This must also be done on the basis of some empirical characteristics, but these characteristics are developed by the theory of evolution. Charles Darwin's[15] main contribution to classification theory of not just his claim "... all true classification is genealogical ..." but that he provided operational guidance for classification.[16]: 90–92 Genealogical classification is not restricted to biology, but is also much used in, for example, classification of languages, and may be considered a general approach to classification." These methods may overall be related to the historicist theory of knowledge. One of the main schools of historical classification is cladistics, which is today dominant in biological taxonomy, but also applied to other domains.

The historical and hermeneutical approaches is not restricted to the development of the object of classification (e.g., animal species) but is also concerned with the subject of classification (the classifiers) and their embeddedness in scientific traditions and other human cultures.

Pragmatic, functionalist and teleological approaches[edit]

Pragmatic classification (and functional[17] and teleological classification) is the classification of items which emphasis the goals, purposes, consequences,[18] interests, values and politics of classification. It is, for example, classifying animals into wild animals, pests, domesticated animals and pets. Also kitchenware (tools, utensils, appliances, dishes, and cookware used in food preparation, or the serving of food) is an example of a classification which is not based on any of the above-mentioned three methods, but clearly on pragmatic or functional criteria. Bonaccorsi, et al. (2019) is about the general theory of functional classification and applications of this approach for patent classification.[17] Although the examples may suggest that pragmatic classifications are primitive compared to established scientific classifications, it must be considered in relation to the pragmatic and critical theory of knowledge, which consider all knowledge as influences by interests.[19]

Ridley (1986) wrote:[20]: 191 "teleological classification. Classification of groups by their shared purposes, or functions, in life - where purpose can be identified with adaptation. An imperfectly worked-out, occasionally suggested, theoretically possible principle of classification that differs from the two main such principles, phenetic and phylogenetic classification".

Examples of important classification systems[edit]

Periodic table[edit]

The periodic table is the classification of the chemical elements which is in particular associated with Dmitri Mendeleev (cf., History of the periodic table). An authoritative work on this system is Scerri (2020).[21] Hubert Feger (2001; numbered listing added) wrote about it:[22]: 1967–1968 "A well-known, still used, and expanding classification is Mendeleev's Table of Elements. It can be viewed as a prototype of all taxonomies in that it satisfies the following evaluative criteria:

Theoretical foundation: A theory determines the classes and their order.

Objectivity: The elements can be observed and classified by anybody familiar with the table of elements.

Completeness: All elements find a unique place in the system, and the system implies a list of all possible elements.

Simplicity: Only a small amount of information is used to establish the system and identify an object.

Predictions: The values of variables not used for classification can be predicted (number of electrons and atomic weight), as well as the existence of relations and of objects hitherto unobserved. Thus, the validity of the classification system itself becomes testable."

Bursten (2020) wrote, however "Hepler-Smith, a historian of chemistry, and I, a philosopher whose work often draws on chemistry, found common ground in a shared frustration with our disciplines’ emphases on the chemical elements as the stereotypical example of a natural kind. The frustration we shared was that while the elements did display many hallmarks of paradigmatic kindhood, elements were not the kinds of kinds that generated interesting challenges for classification in chemistry, nor even were they the kinds of kinds that occupied much contemporary critical chemical thought. Compounds, complexes, reaction pathways, substrates, solutions – these were the kinds of the chemistry laboratory, and rarely if ever did they slot neatly into taxonomies in the orderly manner of classification suggested by the Periodic Table of Elements. A focus on the rational and historical basis of the development of the Periodic Table had made the received view of chemical classification appear far more pristine, and far less interesting, than either of us believed it to be."[23]

Linnaean taxonomy[edit]

Linnaean taxonomy is the particular form of biological classification (taxonomy) set up by Carl Linnaeus, as set forth in his Systema Naturae (1735) and subsequent works. A major discussion in the scientific literature is whether a system that was constructed before Charles Darwin's theory of evolution can still be fruitful and reflect the development of life.[24][25]

Astronomy[edit]

Astronomy is a fine example on how Kuhn's (1962) theory of scientific revolutions (or paradigm shifts) influences classification.[26] For example:

Paradigm one: Ptolemaic astronomers might learn the concepts "star" and "planet" by having the Sun, the Moon, and Mars pointed out as instances of the concept “planet” and some fixed stars as instances of the concept “star.”

Paradigm two: Copernicans might learn the concepts "star", "planet", and "satellites" by having Mars and Jupiter pointed out as instances of the concept “planet,” the Moon as an instance of the concept “satellite,” and the Sun and some fixed stars as instances of the concept "star". Thus, the concepts "star", "planet", and "satellite" got a new meaning and astronomy got a new classification of celestial bodies.

Hornbostel–Sachs classification of musical instruments[edit]

Hornbostel–Sachs is a system of musical instrument classification devised by Erich Moritz von Hornbostel and Curt Sachs, and first published in 1914.[27] In the original classification, the top categories are:

Idiophones: instruments that rely on the body of the instrument to create and resonate sound.

Membranophones: instruments that have a membrane that is stretched over a structure, often wood or metal, and struck or rubbed to produce a sound. The subcategories are largely determined by the shape of the structure that the membrane is stretched over.

Chordophone: Instruments that use vibrating strings, which are most commonly stretched across a metal or wooden structure, to create sound.

Aerophones Instruments that require air passing through, or across, them to create sound. Most commonly constructed of wood or metal.

A fifth top category,

Electrophones: Instruments that require electricity to be amplified and heard. This group was added by Sachs in 1940.

Each top category is subdivided and Hornbostel-Sachs is a very comprehensive classification of musical instruments with wide applications. In Wikipedia, for example, all musical instruments are organized according to this classification.

In opposition to, for example, the astronomical and biological classifications presented above, the Hornbostel-Sachs classification seems very little influenced by research in musicology and organology. It is based on huge collections of musical instruments, but seems rather as a system imposed upon the universe of instruments than as a system with organic connections to scholarly theory. It may therefore be interpreted as a system based on logical division and rationalist philosophy.

Diagnostic and Statistical Manual of Mental Disorders (DSM)[edit]

Diagnostic and Statistical Manual of Mental Disorders (DSM) is a classification of mental disorders published by the American Psychiatric Association (APA).The first edition of the DSM was published in 1952,[28] and the newest, fifth edition was published in 2013.[29] In contrast to, for example, the periodic table and the Hornbostel-Sachs classification, the principles for classification have changed much during its history. The first edition was influenced by psychodynamic theory, The DSM-III, published in 1980[30] adopted an atheoretical, “descriptive” approach to classification[31] The system is very important for all people involved in psychiatry, whether as patients, researchers or therapists (in addition to insurance companies), but the systems is strongly criticized and has not the scientific status as many other classifications.[32]

Philosophical issues[edit]

Artificial versus natural classification[edit]

Natural classification is a concept closely related to the concept natural kind. Carl Linnaeus is often recognized as the first scholar to clearly have differentiated "artificial" and "natural" classifications[33][34] A natural classification is one, using Plato's metaphor, that is “carving nature at its joints”[35] Although Linnaeus considered natural classification the ideal, he recognized that his own system (at least partly) represented an artificial classification.

John Stuart Mill explained the artificial nature of the Linnaean classification and suggested the following definition of a natural classification:"The Linnæan arrangement answers the purpose of making us think together of all those kinds of plants, which possess the same number of stamens and pistils; but to think of them in that manner is of little use, since we seldom have anything to affirm in common of the plants which have a given number of stamens and pistils."[36]: 498 "The ends of scientific classification are best answered, when the objects are formed into groups respecting which a greater number of general propositions can be made, and those propositions more important, than could be made respecting any other groups into which the same things could be distributed."[36]: 499 "A classification thus formed is properly scientific or philosophical, and is commonly called a Natural, in contradistinction to a Technical or Artificial, classification or arrangement."[36]: 499 Ridley (1986) provided the following definitions:[20]

"artificial classification. The term (like its opposite, natural classification) has many meanings; in this book I have picked a phenetic meaning. A classificatory group will be defined by certain characters, called defining characters; in an artificial classification, the members of a group resemble one another in their defining characters (as they must, by definition) but not in their non-defining characters. With respect to the characters not used in the classification, the members of a group are uncorrelated.

"natural classification. Classificatory groups are defined by certain characters, called 'defining' characters; in a natural group, the members of the group resemble one another for non-defining characters as well as for the defining character. This is not the only meaning for what is perhaps the most variously used term in taxonomy ...

Taxonomic monism vs. pluralism[edit]

Stamos (2004)[37]: 138 wrote: "The fact is, modern scientists classify atoms into elements based on proton number rather than anything else because it alone is the causally privileged factor [gold is atomic number 79 in the periodic table because it has 79 protons in its nucleus]. Thus nature itself has supplied the causal monistic essentialism. Scientists in their turn simply discover and follow (where "simply" ≠ "easily")."

List of classification systems[edit]

Business, organizations, and economics[edit]

Classification of customers, for marketing (as in Master data management) or for profitability (e.g. by Activity-based costing)

Classified information, as in legal or government documentation

Job classification, as in job analysis

Standard Industrial Classification, economic activities

Mathematics[edit]

Attribute-value system, a basic knowledge representation framework

Classification theorems in mathematics

Mathematical classification, grouping mathematical objects based on a property that all those objects share

Statistical classification, identifying to which of a set of categories a new observation belongs, on the basis of a training set of data

Media[edit]

Classification (literature), a figure of speech linking a proper noun to a common noun using the or other articles

Decimal classification, decimal classification systems

Document classification, a problem in library science, information science and computer science

Classified information, sensitive information to which access is restricted by law or regulation to particular classes of people

Library classification, a system of coding, assorting and organizing library materials according to their subject

Image classification in computer vision

Motion picture rating system, for film classification

Science[edit]

Scientific classification (disambiguation)

Biological classification of organisms

Chemical classification

Medical classification, the process of transforming descriptions of medical diagnoses and procedures into universal medical code numbers

Taxonomic classification, also known as classification of species

Cladistics, an approach using similarities

Other[edit]

An industrial process such as mechanical screening for sorting materials by size, shape, density, etc.

Civil service classification, personnel grades in government

Classification of swords

Classification of wine

Locomotive classification

Product classification

Security classification, information to which access is restricted by law or regulation

Ship classification society, a non-governmental organization that establishes and maintains technical standards for the construction and operation of ships and offshore structures

Organizations involved in classification[edit]

International Society for Knowledge Organization

CLASSIFICATION | English meaning - Cambridge Dictionary

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English (UK)

English

Meaning of classification in English

classificationnoun uk

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/ˌklæs.ɪ.fɪˈkeɪ.ʃən/ us

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C2 [ U ] the act or process of dividing things into groups according to their type: Do you understand the system of classification used in ornithology?

C2 [ C ] a group that something is divided into

SMART Vocabulary: related words and phrases

Classifying and creating order

alphabetize

anti-hierarchical

arrange

arrangement

arranger

concordance

describe

macrocosm

misclassification

misclassify

miscode

mislabel

misorder

pigeonhole

short-list

shortlist

sort

sort something out

spring-clean

unstructured

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Categories and varieties

(Definition of classification from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)

classification | American Dictionary

classificationnoun [ C/U ] us

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the division of things into groups by type: [ U ] The new pay classification takes effect next week. [ C ] Hotels are listed in four classifications from economy to deluxe.

biology Classification is also the division of organisms into groups according to particular characteristics.

(Definition of classification from the Cambridge Academic Content Dictionary © Cambridge University Press)

classification | Business English

classificationnoun [ U ] uk

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/ˌklæsɪfɪˈkeɪʃən/ us

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the process of organizing things such as jobs or products into particular groups based on their type: Second-tier employees currently start at $7.55 to $11.05 an hour, depending on the job classification.

TRANSPORT the process of checking a ship's condition and equipment in order to make certain that they are safe and meet the official standards of the shipping industry: Ship classification is essential to the safe-guarding of life, property, and the environment

(Definition of classification from the Cambridge Business English Dictionary © Cambridge University Press)

Examples of classification

classification

Two survey categories were underspecified for our purposes, and we used socioeconomic data to check the validity of our classifications.

From the Cambridge English Corpus

Thus, he concludes that classifications of verbs based on theta-roles are misconceived.

From the Cambridge English Corpus

In fact, these industry classifications are very broad and the relevant conditions of interest could occur at a finer level of disaggregation, or across industries.

From the Cambridge English Corpus

In addition, traditional classifications based on morphological characters do not necessarily represent the phylogeny of filarial nematodes.

From the Cambridge English Corpus

If both the highly suitable and suitable classifications are selected, a crop list will be provided showing all highly suitable and suitable crops.

From the Cambridge English Corpus

Comparisons of functions could be based on suggested classifications of functions.

From the Cambridge English Corpus

Given the categorical nature of these classifications, they were assigned dummy weightings and analyzed with point-biserial correlations.

From the Cambridge English Corpus

Associations with the four group classifications were examined by cross tabulation and tested for significance by chi-square.

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To lend empirical support for the viability of the classifications, we assessed correlations of the classifications with word classes.

From the Cambridge English Corpus

As applied here, the observed variables are the classifications assigned by the judges.

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We can see that all tables show evidence of confusion among the classifications.

From the Cambridge English Corpus

We find here the introduction of artificial intelligence, and the attempt to create meaningful classifications of sound which would aid the principles of synthesis.

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Such classifications of knowledge came into existence with a view to how they would fit with bureaucracies.

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On the other hand, when an institution fails to make correct or appropriate classifications, the very legitimacy of the institution is at stake.

From the Cambridge English Corpus

Allowing for multiple-race responses requires new thinking about the very purposes of racial classifications in the first place.

From the Cambridge English Corpus

See all examples of classification

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.

Collocations with classification

classification

These are words often used in combination with classification.Click on a collocation to see more examples of it.

automatic classificationApplications of the system include automatic classification of environmental sounds, musical instruments, music genre and human speakers.

From the Cambridge English Corpus

basis of classificationThe basis of classification will be discussed below.

From the Cambridge English Corpus

binary classificationThe approach achieved an accuracy of approximately 80% on the binary classification task.

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What is the pronunciation of classification?

C2,C2

Translations of classification

in Chinese (Traditional)

將…分類，將…歸類, 把…分級, 類別，等級，門類…

in Chinese (Simplified)

将…分类，将…归类, 把…分级, 类别，等级，门类…

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clasificación, clasificación [feminine]…

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classificação, classificação [feminine]…

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वर्गीकरण - वस्तूंच्या प्रकारानुसार गटांमध्ये विभागण्याची कृती किंवा प्रक्रिया…

分類, 分類（ぶんるい）…

tasnif, sınıflandırma, gruplandırma…

classification [feminine], classification…

classificació…

indeling…

பொருள்களை அவற்றின் வகைக்கேற்ப குழுக்களாகப் பிரிக்கும் செயல் அல்லது செயல்முறை…

वर्गीकरण…

વર્ગીકરણ…

kategorisering, inddeling, klassificering…

klassifikation, klassificering…

pengelasan…

die Einteilung…

klassifikasjon [masculine], inndeling [masculine], klassifisering…

درجہ بندی, مزرہ بندی…

класифікація, визначення категорій…

классификация…

వర్గీకరణ…

تَصنيف…

শ্রেণি বিন্যাস বা বিভাজন…

klasifikace, (roz)třídění…

klasifikasi…

การจัดกลุ่ม…

sự phân loại…

klasyfikacja…

분류…

classificazione…

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Dictionary > Classification system

Classification system

n., plural: classification systems

[ˌklæsɪfɪˈkeɪʃən ˈsɪstəm]

Definition: the systematic placement of organisms into groups or taxonomic rankings

Table of Contents

ToggleClassification Systems DefinitionLevels of the Classification SystemDomainKingdomPhylumClassOrderFamilyGenusSpeciesExamples of classification systemsQuizSend Your Results (Optional)Reference

Classification Systems Definition

In life, many things are classified, that is, to put into categories or groups based on their characteristics. Of course, biology, being the study of life and living things, also has an order of classification. The classification of living things helps us in many ways to organize and group organisms based on their characteristics.

To further delve into this system, we must first define it. What is a classification system? How would one define a classification system? The classification system is the system used for the scientific classification of organisms and other activities in science based on the characteristics, behaviors, and methods used.

Would you like to understand how classification system works? Join us and participate in our Forum discussion: What is phylum chordata? Our community may be able to help!

There are different types of classification systems and they are all used for different purposes. Organism classification takes place in the form of a taxonomic system. This is called the Linnean classification. The Linnean classification involves the usage of the grouping organisms using a hierarchy called taxa. This animal classification system contains taxonomic levels and taxonomic groups that animals are placed in based on their features and even shared ancestry.

These levels of biological classification are as follows:

Species » Genus » Family » Order » Class » Phylum » Kingdom » Domain

These were listed from the least inclusive to the most inclusive. Figure 1 below shows the taxonomical ranking.

Figure 1: The hierarchy of different taxonomic ranks in the Biological Classification System. Source: Akanksha Saxena of Biology Online.

Biology definition:

The classification system is a system for classifying things, particularly, the collection of procedures, characteristics, and definitions used to classify and/or identify things. The levels of biological classification are as follows: Species » Genus » Family » Order » Class » Phylum » Kingdom » Domain (from least- to most-inclusive).

Levels of the Classification System

The classification of organisms takes place in the different taxonomic levels. They will be defined and listed according to their inclusiveness in groups.

Domain

The domain classification is the highest level of taxonomic classification in the organism classification system. The domain can be broken down into three types: Archaea domain, Eukaryotic domain, and the (Eu)Bacteria domain. These can be seen in Figure 2 below. These individual domains are based on their evolution over the years and the different attributes they contain.

Bacteria are also known as prokaryotes as they have no intracellular organelles and do not contain a nucleus. Archaea, though similar to bacteria are quite different. They are genetically distinct from each other. Last but not least, eukarya is the last domain. The organisms that belong to this domain have membrane-bound organelles and nuclei. This makes them easier able to complete tasks and be more efficient as they have divided the tasks among different organelles, making them specified.

Figure 2: The three domains of life. Diagram Source: Maria Victoria Gonzaga of Biology Online.

Kingdom

The kingdom classification is the second-highest ranking in the taxonomic groupings of organisms. How many kingdoms are there? There are five kingdoms, though some recent studies have claimed six and seven kingdoms. The five kingdoms consist of the animals, plants, fungi, protists, and monerans.

The kingdom Animalia is the most diverse out of the kingdoms and this is because it has evolved the most. This kingdom is generally divided into invertebrates and vertebrates (animals that have a backbone and those that do not).

Chordates are animals that belong to Kingdom Animalia. Join us and participate in our Forum: What is phylum chordata? Learn more about them today!

The kingdom Plantae is made up of all trees, flowers, bushes, and vegetation. It is the oldest of all the kingdoms. Its members are characterized by having limited movement, eukaryotic features, and autotrophic abilities.

Yeasts, toadstools, molds and mushrooms belong to the kingdom Fungi. These organisms are carnivores that have chitin in their cell walls yet reproduce in a sporic manner.

Protista can be considered the mother of all eukaryotes as all of them are descendants of this kingdom. It can be a very difficult kingdom to distinguish as it is intertwined with many of the others. The monera kingdom consists of all archaea and bacteria as it deals with all microscopic organisms. The kingdoms can be clearly seen in Figure 3 below.

Figure 3: An illustration depicting the diversity of living organisms classified into 5 major kingdoms with various phyla according to the 5-Kingdom classification system of Robert Whittaker. Credit: Iberdrola.

Phylum

In the kingdom-phylum ranking system, the next classification is phylum. This taxonomic rank, sometimes termed as “division” lies after the kingdom and further classifies based on phenetic and phylogenetic. Phenetics is based on the number of shared characteristics using a numerical system and phylogenetics is based on evolution and shared relationships but using a systematic study. Each kingdom is broken down into numerous phyla. This can range from as few as four like in Kingdom Protista to as many as the nine phyla that kingdom Animalia contains.

Class

The class falls just between the phylum and order classifications. Just like kingdoms contain multiple phyla, each phylum can contain multiple classes. These generally end with the suffix “ae” when they are named. Sometimes, if classes are very large, they may be divided into subclasses.

Order

Order is the classification that consists of several families. Orders above the family classification and below the ranking of classes. An order consists of multiple families that share many characteristics and evolutionary traits.

Family

When a group of genera with similar characteristics and traits are pulled together it is called a family. The family is the ranking between orders and genus in the Linnean classification. Multiple genera make up a family group.

Genus

Genus is the systematic unit in the organism classification that helps determine the species of organisms as the genus groups multiple species together. A genus could also consist of one unusual species whose attributes are so unique it is classified on its own.

Species

Species classification is the final ranking for the biological classification of living things. A species is defined as a group of organisms with similar characteristics that are able to procreate or interbreed with one another. The offspring they produce must be sustainable and also being able to create a new generation of the species as well. Sometimes, species can form evolve into another, this is known as speciation. Figure 4 above shows the speciation of the Galapogos Finches.

Figure 4: The speciation of Galapagos Finches. Diagram Source: Maria Victoria Gonzaga of Biology Online.

Examples of classification systems

The classification of systems is used to scientifically name organisms based on genus and species. For instance, the scientific name for humans is Homo sapiens sapiens. “Homo” coming from the genus and “sapiens sapiens” being the species.

All organisms can be classified based on the classification system. For instance, a simple household pet such as a cat. A cat would belong to the domain eukarya, being a multicellular organism. This would be further divided into the kingdom Animalia as a cat is obviously an animal. Being an animal that has a flexible rod that supports its backbone, it would be a member of the phylum Chordata.

Phylum Chordata – a phylum consisting of all chordates. Find out which animals belong in this group: What is phylum chordata? Join now!

The class of the domestic cat would be Mammalia being an organism that carries its young in a womb and also lactates to feed its offspring. The house cat then follows the path of being a member of the order Carnivora and the family of Felidae. Finally, we come to the genus, which in this case is Felis and the species is catus. So a cat, using the classification system is called Felis catus.

Figure 5 Classification and scientific name of domestic cat. Image Source Maria Victoria Gonzaga of Biology Online.

Try to answer the quiz below to check what you have learned so far about the classification system.

Quiz

Choose the best answer.

1. The systematic placement of organisms into groups or taxa Classification system Distribution system Ecosystem

2. The correct increasing taxonomic ranks Species > Genus > Family > Order > Phylum > Domain > Kingdom Species > Genus > Family > Phylum > Order > Kingdom > Domain Species > Genus > Family > Order > Phylum > Kingdom > Domain

3. The domain consisting of true bacteria Archaea Eubacteria Eukaryota

4. Second-highest ranking in the taxonomic groupings of organisms Domain Kingdom Species

5. The taxonomic rank consisting of organisms that are able to procreate or interbreed with one another Domain Kingdom Species

Send Your Results (Optional)

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Reference

Biology Dictionary Editors. (2019). Domain. Biology Dictionary.

Biology Online. (2021). Classification System Defintion. Biology Online. https://www.biologyonline.com/dictionary/classification-system

Biology Online. (2021). Phylum. Biology Online. https://www.biologyonline.com/dictionary/phylum

Carr, S. (2019). Phenetic vs Phylogentic classification of birds. MUN. https://www.mun.ca/biology/scarr/Phenetic_vs_Phylogenetic_classification_of_Birds.html

CDN. (2021). Taxonomy of the cat. CDN. https://cdn.citl.illinois.edu/courses/ANSC207/week1/Domestication/web_data/file12.htm

Gittleman, J. L. (2019). Species. Encyclopedia Britannica. https://www.britannica.com/science/species-taxon

Iberdrola. (2021). Biology 5 Kingdoms of Living things. Iberdrola. https://www.iberdrola.com/sustainability/biology-kingdoms-living-things-classification

Scitable. (2014). Species. Nature Education. https://www.nature.com/scitable/definition/species-312/

Last updated on May 29th, 2023

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CLASSIFICATION Definition & Usage Examples | Dictionary.com

GamesDaily CrosswordWord PuzzleWord FinderAll gamesFeaturedWord of the DaySynonym of the DayWord of the YearNew wordsLanguage storiesAll featuredPop cultureSlangEmojiMemesAcronymsGender and sexualityAll pop cultureWriting tipsGrammar Coach™Writing hubGrammar essentialsCommonly confusedAll writing tipsGamesFeaturedPop cultureWriting tipsclassification[ klas-uh-fi-key-shuhn ]show ipaSee synonyms for: classificationclassificatory on Thesaurus.comnounthe act of classifying. the result of classifying or being classified. one of the groups or classes into which things may be or have been classified. Biology. the assignment of organisms to groups within a system of categories distinguished by structure, origin, etc. The usual series of categories is phylum (or, especially in botany, division), class, order, family, genus, species, and variety.the category, as restricted, confidential, secret, or top secret, to which information, a document, etc., is assigned, as by a government or military agency, based on the degree of protection considered necessary to safeguard it from unauthorized use.Library Science. any of various systems for arranging books and other materials, especially according to subject or format.See moreOrigin of classification11780–90;

Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024How to use classification in a sentenceThis week, we’re looking at the latest developments in the battle over the classification of gig workers, the rise of labor unions in tech and and Instagram’s latest move to be woke.Human Capital: The battle over the fate of gig workers continues | Megan Rose Dickey | September 11, 2020 | TechCrunchIt would soon become clear that this classification was, at best, misleading.The Mess That Is the 2020 James Beard Awards, Explained | Elazar Sontag | September 11, 2020 | EaterMathematicians pursue this classification with “cohomology” theories, which allow them to extract algebraic fingerprints from complicated geometric spaces.The Mathematical Structure of Particle Collisions Comes Into View | Charlie Wood | August 20, 2020 | Quanta MagazineThese two companies have been sued many, many times for their labor practices, specifically as they pertain to the classification of their respective drivers as independent contractors.Human Capital: Uber and Lyft’s ongoing battle with the law and a brief history of diversity at Snap | Megan Rose Dickey | August 7, 2020 | TechCrunchThese classifications may be revisited if a sponsor ceases engaging in this behavior.Polls Policy And FAQs | Dhrumil Mehta (dhrumil.mehta@fivethirtyeight.com) | July 17, 2020 | FiveThirtyEightYet much of the best new music defies genre classification; great artists take chances and cross boundaries.Five Lessons the Faltering Music Industry Could Learn From TV | Ted Gioia | August 3, 2014 | THE DAILY BEASTStill, Wallace said that no one at the meeting involving Fearey, which he also attended, raised classification concerns.Fired From Los Alamos for Pushing Obama's Nuclear Agenda | Center for Public Integrity | July 31, 2014 | THE DAILY BEAST“The classification system, of course, is not supposed to be used for political purposes,” Bunn said.Fired From Los Alamos for Pushing Obama's Nuclear Agenda | Center for Public Integrity | July 31, 2014 | THE DAILY BEASTBut Doyle said Fearey never raised any concerns about classification.Fired From Los Alamos for Pushing Obama's Nuclear Agenda | Center for Public Integrity | July 31, 2014 | THE DAILY BEASTLambic represents the parent classification for a host of sub-categories.Wine Snobs, There’s a Beer for You | Jordan Salcito | April 5, 2014 | THE DAILY BEASTHis hero, Gulliver, discovers race after race of beings who typify the genera in his classification of mankind.Gulliver's Travels | Jonathan SwiftIn addition to the tolls and charges, the Acts usually contained a rough classification of goods to which they applied.Fifty Years of Railway Life in England, Scotland and Ireland | Joseph TatlowWhen the child entered the workhouse it passed out of its former classification and entered into an entirely different one.English Poor Law Policy | Sidney WebbBy 1860 it "had given instructions that every new workhouse should be so constructed as to allow of the requisite classification."English Poor Law Policy | Sidney WebbIn some later writers on music we find this classification reduced to a more regular form, and clothed in technical language.The Modes of Ancient Greek Music | David Binning MonroSee More ExamplesBritish Dictionary definitions for classificationclassification/ (ˌklæsɪfɪˈkeɪʃən) /nounsystematic placement in categoriesone of the divisions in a system of classifyingbiology the placing of animals and plants in a series of increasingly specialized groups because of similarities in structure, origin, molecular composition, etc, that indicate a common relationship. The major groups are domain or superkingdom, kingdom, phylum (in animals) or division (in plants), class, order, family, genus, and speciesthe study of the principles and practice of this process; taxonomygovernment the designation of an item of information as being secret and not available to people outside a restricted groupSee moreOrigin of classification1C18: from French; see class, -ify, -ationDerived forms of classificationclassificational, adjectiveclassificatory, adjectiveCollins English Dictionary - Complete & Unabridged 2012 Digital Edition

Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012Scientific definitions for classificationclassification[ klăs′ə-fĭ-kā′shən ]The systematic grouping of organisms according to the structural or evolutionary relationships among them. Organisms are normally classified by observed similarities in their body and cell structure or by evolutionary relationships based on the analysis of sequences of their DNA. See more at cladistics Linnean. See Table at taxonomy.The American Heritage® Science Dictionary

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Classification | Internet Encyclopedia of Philosophy

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Classification

One of the main topics of scientific research is classification. Classification is the operation of distributing objects into classes or groups—which are, in general, less numerous than them. It has a long history that has developed during four periods: (1) Antiquity, where its lineaments may be found in the writings of Plato and Aristotle; (2) The Classical Age, with natural scientists from Linnaeus to Lavoisier; (3) The 19th century, with the growth of chemistry and information science; and (4) the 20th century, with the arrival of mathematical models and computer science. Since that time, and from an extensional viewpoint, mathematics, specifically, the theory of orders and the theory of graphs or hypergraphs, has facilitated the precise study of strong and weak forms of order in the world, and the computation of all the possible partitions, chains of partitions, covers, hypergraphs or systems of classes that we can construct on a domain. With the development of computer science, Artificial Intelligence, and new kinds of languages such as oriented-objected languages, an intensional approach has completed the previous one. Ancient discussions between Aristotle and Plato, Ramus and Pascal, Jevons and Joseph found some kind of revival via object-oriented modeling and programming, most of objected oriented languages being concerned with hierarchies, or partial orders: these structures reflect in fact the relations between classes in those languages, which generally admit single or multiple inheritance. In spite of these advances, most of classifications are still based on the evaluation of resemblances between objects that constitute the empirical data. This one is almost always computed by the means of some notion of distance and of some algorithms of aggregation of classes. So all these classifications remain, for technical and epistemological reasons that are detailed below, very unstable ones. A real algebra of classifications, which could explain their properties and the relations existing between them, is lacking. Though the aim of a general theory of classifications is surely a wishful thought, some recent conjecture gives the hope that the existence of a metaclassification (or classification of all classification schemes) is possible.

Table of Contents

General Introduction: Classification Problems

A Brief History of Classifications

From Antiquity to the Renaissance

From Classical Age to Victorian Taxonomy

The Beginning of Modernity

The Problem of Information Storage and Retrieval

Ranganathan and the PMEST Scheme

Order and Mathematical Models

Extensional Structures

A Glance at an Intensional Approach

The Idea of a General Theory of Classifications

References and Further Readings

1. General Introduction: Classification Problems

Classification problems are one of the basic topics of scientific research. For example, mathematics, physics, natural sciences, social sciences and, of course, library and information sciences all make use of taxonomies. Classification is a very useful tool for ordering and organization. It has increased knowledge and helped to facilitate information retrieval.

Roughly speaking, ‘classification’ is the operation consisting of sharing, distributing or allocating objects in classes or groups which are, in general, less numerous than them. Commonly, classifications are defined on finite sets. However, if the objects are, for example, mathematical structures there can be infinite classifications. In this case, the previous requirement, of course, must be weakened: we may only want the (infinite) cardinal of the classification to be less than or equal to the (infinite) cardinal of the set of objects to be classified. What we call ‘classification’ is also the result of this operation. We want, as much as it is possible, for this result be constant, namely, that the classification itself remains stable for a little transformation of data (of course, the sense of this requirement will have to become clearer). Various situations may happen: the classes may intersect or not, be finite or infinite, formal or fuzzy, hierarchically ordered or not, and so on.

The basic operation of grouping elements into classes, which simplifies the world, is a very powerful operation, but it also raises many questions. In particular, a number of philosophers, from Socrates to Diderot and even post-modern philosophers, criticized such an operation (see, for instance, Foucault 1967). Indeed, this operation has multiple profits. First is the substitution of a rational and regular order in the chaotic and muddled multiplicities. Second is the reduction of the size of sets, so that, once we have constituted classes of equivalences, we can work with these classes and no more with the elements. Third, and finally, to make a partition of a set means locating in it a symmetry that decreases the complexity of the problem and so simplifies the world. We can say with Dagognet (1984, 1990) than “less is more”: to compress the data really brings an intellectual gain.

Having outlined the main reasons for classifications, let us see how these classifications have developed and which forms they got throughout the course of time.

2. A Brief History of Classifications

The history of classifications (Dahlberg 1976) develops in four periods. From Plato and Aristotle to the 18th century, ancient classifications are hierarchical ones, they are finite and generally based on one single criterion. During the 18th century, some new classifications appear, which are multicriteria – a domain can be co-divided in many ways, as Kant said in his Logic (see Kant 1988) – and indefinite or virtually infinite (Kant believed that we could endlessly subdivide the extension of a concept). At the end of the 18th and at the beginning of the 19th century, with the chemical classifications of Lavoisier and then of Mendeleyev, one discovers combinatorial classifications or multiple crossed orders, like the chemical table of Elements, which correspond to a new concept of classification. In the 20th century, through the progress of mathematical order theory, factorial analysis of correspondence, and automatic classification, formal models begin to develop.

a. From Antiquity to the Renaissance

French commentator of Greek philosophers, R. Joly said that a typical trend of the Greek spirit was to reduce a multiple and complex reality into some categories which satisfy the reason, both by their restricted number and by the clear and precise sense that becomes attached to each of them. Indeed, Plato and Aristotle are among the great classifiers of these ancient times.

In all of Plato’s Dialogues, and especially in the latest ones (Parmenides, Sophist, Politicus, Philaebus), Plato obviously classified a lot of things (ways of life, political constitutions, pleasures, arts, jobs, kinds of knowledge, and so forth). Generally, for Plato, things were classified in relation with the distance that separates them from their archetypal forms, which yields some order (or pre-order) on them. Plato’s classifications are finite, hierarchical, dichotomous, and based on a single criterion. For example, in Gorgias (465c), a set of all practices is divided into two classes, the practices concerning the body and the practices concerning the soul, each of them being then divided into two others: gymnastics and medicine, on one hand, and legislation and justice, on the other hand. In the same way, in Republic (510a), the whole universe, viewed as the set of all real things, is divided into the visible world and the invisible world, each class being subdivided into images and objects or living beings on one hand, mathematical objects and ideas, on the other hand.

According to Plato, the rules of classifications are very simple. First, we have to make symmetric divisions in order to get well-balanced classes. For example, if we classify the peoples, we have to avoid setting the Greek in front of the other peoples, because one of the classes will be plethoric while the other one will have only one element (Politicus, 262a). Second, As a good cook who cuts an animal─this metaphor is in the Phaedrus−it is also necessary to choose the good joints or articulations. For example, in the field of numbers, it would be senseless to set 1000 in front of 999 other numbers. In contrast, the opposition even/odd or prime/not prime, is a real one. Thirds, in general, we must also avoid using negative determinations. For example, we have to avoid determinations like not-A because it is impossible that the non-being has sorts or species, these determinations block the development of thought.

Plato did not observe these wise rules, so incurring Aristotle’s criticisms. Against Plato’s theory, Aristotle argues that the method of division is not a powerful tool because it is non-conclusive. It does not make syllogisms (First Analytics, I, 31). In another text (Second Analytics, II,5), Aristotle insists on the contingency of the passage from a predicate to another one, that is, in the Platonic division, for every new attribute, we can wonder why it is such an attribute oppose to another one. The differences introduced by dichotomies can be also purely negative and thus do not necessarily define a real being. Moreover, binary divisions presuppose that the number of the primitive species is a power of 2. In a division, a predicate can belong to different primitive species, for example “bipedalism” can apply to both birds and humans. But, according to Aristotle, the application of this term is not the same in both cases. Finally, the Platonic division confuses extensional and intensional views. It can identify the triangle, which is a kind, and one of its properties, for example, the equality of the sum of its angles in two right angles.

The previous questions get no answer in Plato’s theory. Aristotle rejected Plato’s method of division. But, Aristotle also rejected the Platonic doctrine of forms. According to Aristotle (Metaphysics, I, 9), Plato’s forms fail to explain how there could be permanence and order in the world. Far more, he argued, Plato’s theory of forms cannot explain anything at all in our material world. The properties that the forms have (according to Plato the forms are eternal, unchanging, transcendent, and so forth) are not compatible with material objects and the metaphor of participation or imitation breaks down in a number of cases. For instance, it is unclear what it mean for a white object to participate in, or to copy, the form of whiteness−that is, it is hard to understand the relationship between the form of whiteness and white objects themselves.

For all these reasons, Aristotle develops his own concepts, and his own logic of classifications. In the Topics (I, chap. 1), Aristotle introduces the notions of kind, species, property and a whole theory of basic predication that has subsequently developed in the work of Porphyry and Boece, respectively. This theory is based on the opposition between essence, all of the characters that define a thing, and accident, the qualities whose presence or absence does not modify the things essence. A commentator of the Aristotelian system, Porphyry (234-305), puts these distinctions to good use and tries to specify the hierarchy of the kinds and the species as defined by Aristotle. The famous Porphyrian Tree is the first abstract tree outlining these distinctions and illustrates the subordination existing between them (See Figure 1).

Figure 1: The Porphyrius Tree

In a passage of his Commentary on Aristotle’s Categories (2014) Porphyry asked good questions at the origin of a hotly-debated controversy over whether or not universals were physical or immaterial substances. That is, a contention over whether universals are separated from sensible things or if they are involved in them, finding their consistency therein. In opposition to the traditional views (Platonic and Aristotelian or scholastic realisms), other solutions appeared. For example, Nominalism (Roscelin, 11th c.) claimed that universals are but words and that nothing corresponds to them in the Nature, which knows only the singular. Against that was Conceptualism (Abélard, 12th cn. and Ockham, 14th cn.), the view that kinds exist as predicates of subjects that, themselves, are real. In the last centuries of Middle Ages and in the Renaissance, we find also great scholars who work on classification. In particular, Francis Bacon (1561-1626), whose work on the classification of knowledge that has inspired the great librarians of the 19th century. But, the logic of classifications, which remains, in this time, the Aristotelian logic, receives practically no new development until the 18th century.

b. From Classical Age to Victorian Taxonomy

In the Classical Age, taxonomy as a fully-fledged discipline began to develop for several reasons. One important reason emerges from the birth of natural science and the need to organize floras and faunas in connection with the growth of the human population on Earth, in the context of the beginning of agronomy (Dagognet, 1970). In this period, naturalists like Tournefort (1656-1708), Linnaeus (1707-1778), De Jussieu (1748-1836), Desfontaines (1750-1833) and Cuvier (1769-1832) tried to classify plants and animals all around the world.

When classifying things or beings, you must get a criterion or an index, in order to make classes and separate varieties inside the classes. Indeed, all those naturalists differ on the criteria of their classifications. For example, concerning the classification of plants, Tournefort chose corolla, while Linnaeus chose the sexual organs of the plant. Concerning the animals, the classification of Cuvier violates Aristotle’s recommendations, by compositing vertebrates and invertebrates which, by chance, are something real. At the end of the century, Kant summarizes, in his Logic (1800), the main part of the knowledge about classifications in this period, by specifying the definitions of a certain number of terms and operations that the naturalists of the time empirically use. Kant was only interested in the forms of the classifications. In his Logic he defines a logical division of a concept as “the division of all the possible contained in it”. The rules of this division are the following: 1) members of the division are mutually exclusive, 2) their union restores the sphere of the divided concept, 3) each member of the division can be itself divided (the division of such divided members is a subdivision). (1) and (2) seem to indicate that Kant was approaching our concept of a partition. But (3) shows that he does not have the concept of a chain of partitions, since he does not see that a subdivision of the same level forms one and the same partition.

These problems were also discussed, during the 19th century in Anglo-Saxon countries, even after Darwin’s theory of evolution. One may think that Darwin’s belief in branching evolution was based upon his familiarity with the taxonomy of his day, from which he was very aware. There were great taxonomists in England in the Victorian age and some of them−for instance, the paleontologist H. Alleyne Nicholson, a specialist of British Stromatoporoids−were prodigious and wrote monographs still in force today (Woodward 1903). At approximately the same time, H. Agassiz (Agassiz 1957), a scholar in classification theory, wrote about taxonomic concepts like categories, divisions, forms, homologies, analogies, and so on. Among different taxonomic systems mentioned in his Essay on Classification, include the classical systems of Leeuckart, Vogt, Linnaeus, Cuvier, Lamarck, de Blainville, Burmeister, Owen, Ehrenberg, Milne-Edwards, von Siebold, Stannius, Oken, Fitzinger, MacLeay, von Baer, van Bencden, and van der Hoeven. In The Origin of Species, Darwin himself said that it was a

truly wonderful fact…that all animals and all plants throughout all time and space should be related to each other in group subordinate to group, in the manner which we everywhere behold−namely, varieties of the same species most closely related together, species of the same genus less closely and unequally related together, forming sections and sub-genera, species of distinct genera much less closely related, and genera related in different degrees, forming sub-families, families, orders, subclasses, and classes. (1859, 128)

But what he called the “principle of divergence”–namely, the fact that during the modification of the descendants of any one species and during the incessant struggle of all species to increase in numbers, the more diversified these descendants become, the better will be their chance of succeeding in the battle of life−was illustrated by his famous tree-like diagram sketched in 1837 in the notebook in which he first posited evolution. From this time, tree-like structures, that has been also of great use in chemistry and would be formalized at the end of the century by the mathematician Arthur Cayley, tended to replace classifications.

c. The Beginning of Modernity

A new kind of classifications appeared at the end of the 18th century, with the development of Chemistry, namely, combinatorial classifications or cross multiple orders. This kind of classifications is either the crossing of two or more divisions, or the crossing of two or more hierarchies of divisions. In such a structure, as Granger (1967) said, “elements are distributed according to two or several dimensions, giving rise to a multiplication table”. In a combinatorial classification, the elements themselves are not necessarily distributed into classes. Only the components of these elements are classified. For Granger, this model refers to the Cartesian plane and to the ordinal principle on which it is based. The Cartesian plane, results from a will of ordering a certain distribution of points in the space, by ordering points in every row and then by ordering the rows themselves. The virtue of multiple orders is to place what is classified in the intersection of a line and a column. So, as Dagognet (1969) has shown, when an element is absent or there is an empty compartment, it can be defined by its surroundings. This is what happened in the Mendeleyev table. This table has two main advantages. First, the table is creative, so the mass of a chemical element can be calculated from those which surround it (see Figure 2), and hence, chemical elements, which did not exist in Nature but were synthesized only 30 years later in laboratories, have already been accounted for by Mendeleyev. Second, the classification is not a purely spatial picture of the world. The temporality, in particular the future, is already present in it.

Figure 2: The mass of an unknown element in the Mendeleyev Table

3. The Problem of Information Storage and Retrieval

At the end of the 19th century, the development of scientific research, which raised the question of information storage and retrieval, encouraged the constitution of voluminous librarian catalogues. This included the Dewey’s decimal classification, Otlet and La Fontaine’s universal decimal classification, and the Library of Congress classification. The aim of these kinds of classifications was to account for the whole of knowledge in the world. But, many problems arose from this attempt of library sciences to organize the whole knowledge. Three rules were commonly respected in more natural classifications: 1) Everything classified must appear in the catalogue (which must be, in principle, finite and complete), 2) there is no empty class, 3) nothing can belong to more than one class. Generally, these rules are not respected in library classifications. To face the extraordinary challenge of cataloguing knowledge growing indefinitely throughout the course of time, the big library classifications designed at the end of the 19th century adopted the principle of decimalization. This system was used because decimal numbers, used as numeral items, authorize indefinite extensions of classifications. Suppose you start with 10 main classes, from 0 to 9. If you add a zero to each number, you get the possibility of forming 100 classes (from 00 to 99) and if you go on, you can obtain 1000 classes (from 000 to 999). Then you can also put a comma or a point, and define items like: 150.234. After the point, the sequence of numbers is potentially infinite and you can go as far as is needed. Another difference is that library classifications can sometimes allow for vacant classes in their hierarchy, and also can, assume the inscription of classified subjects in several places. Vacant classes are used because a librarian must manage some place for new documents that are still temporarily unclassified. Multiple inscriptions are also used because readers, who sometimes do not know exactly what they are looking for, need to have a broad ranging accesses to knowledge. This made made way for the existence of entries like author, subject, time, place, and so forth. The previous requirement of decimalization is obvious in the Dewey Decimal Classification (DDC) proposed by Melvil Dewey in 1876 (Béthery 1982). This classification is made up of ten main classes or categories, each of them being divided into ten secondary classes or subcategories. These last ones contain in turn ten subdivisions. The partition of the ten main classes thus gives successively 100 divisions and 1000 sections.

DDC — main sections

000 – Computer Science, Information and General Works

100 – Philosophy and Psychology

200 – Religion

300 – Social Sciences

400 – Language

500 – Science (including Mathematics)

600 – Technology and Applied Science

700 – Arts and Recreation

800 – Literature

900 – History, Geography and Biography

In the same way, the Universal Decimal Classification (UDC) of Otlet and La Fontaine globally presents the same hierarchical organization, except in the fourth nodal class, which is left empty (thus, applying the previous principle of vacant classes).

As librarians have rapidly observed, one undesirable consequence of such decimal schemes is the increasing fragmentation of subjects as taxonomist’s work proceed. For example, the Dewey Classification, though having this useful advantage of being infinitely extendible, turns out rapidly to be a list or a nomenclature. This is also the case of the UDC of Otlet and La Fontaine, and of all the classifications of the same type. A first attempt to make up for such a disadvantage has consisted of allowing some junctions between categories in the classification. A second one is the possibility of using some tables (7 in the DDC) to aid in the search of a complex object, which may be located in different sites. For instance, a book of poetry, written by various poets from around the world, would appear in several classes, indexed thanks to the tables. In general, DDC used to combine elements from different parts of the structure, in order to construct a number representing the subject content. This one often combines 2 or more subject elements with linking numbers and geographical and temporal elements. The method consists of forming a new item rather than drawing upon a list containing each class and its meaning. For example, 330 (for Economics) + 9 (for Geographic Treatment) + 04 (for Europe) and the use of ‘/’ gives 330/94 (European Economy). Another example is the following: 973 (for United States) + 05 (division for periodicals) and the use of the point ‘.’ gives 973.05 (periodicals concerning the United States generally).

Other specific features occur in library classifications, which tend to make them very different from classical scientific taxonomies. One spectacular difference with hierarchical classifications in Zoology or Botany is, as we have already seen, that it is possible for subjects to appear in more than one class. For example, in DDC, a book on Mathematics could appear in the 372.7 section or in the 510 section, depending on if the book is a monograph instruction for teachers on how to teach mathematics, or a mathematics textbook for children. Another difference is a relative flexibility of library classifications.

Though there exist improvements, UDC and DDC, like most of the classifications constructed at the same time (see Bliss 1929) are based on a perception of knowledge and of the relationships between academic disciplines extant from 1890 to 1910. Moreover, though updated regularly, UDC and DDC, as decimal systems, are less hospitable to the addition of new subjects. These kinds of classification are based on fixed and historically dated categories. One may observe, for example, that none of the main concepts of our present library science (digital library, knowledge organization, automatic indexing, information retrieval, and so forth) were included in the index of the 2005 UDC edition, and that technical taxonomies generally require more complex features (Dobrowolski 1964).

4. Ranganathan and the PMEST Scheme

There have been many pursuits to solve the aforementioned librarian problems. Some of them are well known since the middle of the 20th century. In the course of the 20th century, new modes of indexing and original classification schedules appeared in library science with the Indian librarian Shiyali Ramamrita Ranganathan (1933, 2006) and his faceted classification – also called “Colon classification” (CC), because of its use of the colon to indicate relations between subjects in the former edition.

Ranganathan was at first a mathematician and knew little about the library. But he took charge of the Madras University Library, and was then deputed by his University to study Library Science in London. There, he attended the School of Librarianship in the University College and discovered, as he said later, the “charm of classifications”, and also its problems. He saw very quickly that Decimal Classifications did not give satisfaction to users. On the opposite, he had the vision of a meccano set, where, instead of having ready-made rigid toys, one can construct them with a few fundamental components. This made him think of a new kind of classification.

It appeared to Ranganathan that the new theory might be organized at the higher level in 5 fundamental categories (FC) called facets: Personality, Matter, Energy, Space and Time−in summary PMEST. In each isolate facet a Compound Subject is deemed to be a manifestation of one (and only one) of one or other of the five fundamental categories. There is also subfacets, so that the facet scheme PMEST and the subfacets we may form from it, are then used to sort subclasses in the main classes of the classification.

The difference with previous classifications is in the way one defines ‘subfacets’. Rather than simply dividing the main classes into a series of subordinate classes, one subdivides each main class by particular characteristics into facets. Facets, labeled by Arabic numbers, are then combined to make subordinate classes as needed. For example, Literature may be divided by the characteristic of language into the facet of Language, including English, German, and French. It may also be divided by form, which yields the facet of Form, including poetry, drama and fiction. So CC contains both basic subjects and their facets, which contain isolates. A basic subject stands alone, for example: Literature in the subject English Literature, while an isolate, in contrast, is a term that modifies a basic subject, for example, the term ‘English’. Every isolate in every facet must be a manifestation of one of the five fundamental categories in the PMEST scheme.

The advantages of the CC are numerous. The first one is a greater flexibility in determining new subjects and subject numbers. A second is the concept of phases, which allows taxonomists to readily combine most of the main classes in a subject. Consider for example a subject like Mathematics for biologist. In this case, single class number enumerative systems, as those predominating in US libraries, tend to force classifiers to choose either Mathematics or Biology as the main subject. However, CC supplies a specific notation to indicate this be-phased condition.

Indeed, some problems remain unsolved. In CC, facets, that is, small components of larger entities or units are similar to flat faces of a diamond which reflect the underlying symmetry of the crystal structure, so that the general structure of Ranganathan Classification, as that of a faceted classification in general, is a kind of permutohedron. In principle, all descriptions may be done, whatever the order of them. For example, if we have to classify a paper speaking about seasonal variations of the concentration of noradrenaline in the tissue of the rat, we must get the same access if we have the direct sequence: (1) Seasonal, variations, concentration, noradrenaline, tissue, rat, or the reversed one: (2) Rat, tissue, noradrenaline, concentration, variations, seasonal. In mathematical words, this means clearly that the underlying structure that makes this transformation possible must be a commutative group. But this is not always the case, and for some dihedral groups, this structure is even forbidden. Another potential worry is that the PMEST scheme, which certainly has some connections with Indian thought, is far from being universally accepted (see De Grolier 1962) and has not been very often implemented in libraries, even in India.

So, in spite of all the improvements they receive in the course of time, a lot of problems have been raised in front of library classifications. In particular, library classifications will be strongly questioned in the 20th century by the proliferating development of the knowledge. First, the ceaseless flux of new documents forbids a stiff topology for classifications. The problem, then, is to know how to construct evolutionary structures. Second, the successive orderings of the knowledge (groupings and revisions and not only ramifications) has called relational powerful and automated documentary languages. Classifications still remain necessary, because documentary languages cannot do everything. So the problem is still open. But, with the big development of mathematics in the last century, this general problem, which is the great problem of order, has to be investigated by the means of mathematical structures.

5. Order and Mathematical Models

First attempts to study orders in mathematics began to develop at the end of the 19th century with Peano, Dedekind and Cantor (especially with his theory of ordinals, which are linear ordered sets). They go on with Peirce (1880) and Shröder (1890) and their works around the question of an algebra of logic. Then, in the first part of the 20th century, comes the notion of partial order with an article of MacNeille (1937) and the famous work of G. Birkhoff (1967) who introduced the notion of lattice, algebraically developed later in the great book of Rasiowa and Sikorski (1970). During the same period, mathematical models of hierarchical classifications, which have been investigated in the USA by Sokal and Sneath (1963, 1973) or, in England, by Jardine and Sibson (1971) were developed in France in the works of Barbut and Monjardet (1970), Lerman (1970, 1981), and Benzécri (1973). All these works supposed the big last century advances in mathematical order theory: especially the papers of Birkhoff (1935), Dubreil-Jacotin (1939), Ore (1942, 1943), Krasner (1953-1954) and Riordan (1958). The Belgian logician Leo Apostel (1963) and the Polish mathematicians Luszczewska-Romahnowa and Batog (1965a, 1965b) have also published important articles on the subject. The more and more important use of computers in the search of automatic classifications has also been, in those years, a reason for searchers to get interested in mathematical models.

As there are many forms of classifications in the world of knowledge (we can find them, as we have seen, in mathematics, natural sciences, library and information science, and so forth) there are also many possible mathematical models for classifications. We begin with the study of extensional structures.

a. Extensional Structures

In order to clarify the situation, we start with the weakest form of them and move to stronger forms. Mathematics allows us to begin with very few axioms, that usually define weak general structures, and afterwards, by adding new conditions, one can get other properties and stronger models. In our case, the weakest structure is just a hypergraph H = (X,P) in the sense of Berge (1970), with X a set of vertices and P a set of nonempty subsets called edges (See Figure 3).

Figure 3: A Hypergraph

In this case, the set of edges P does not necessarily cover the set X, and some nodes (vertex of degree zero), may have no link to some edge. Assume the following conditions:

(C0) X ∈ P,

(C1) For all x ∈ P, {x} ∈ P,

Accordingly, we have a system of classes (in the sense of Brucker-Barthélemy 2007).

Add now the following new conditions: for every Pi ∈ P:

(C2) Pi ∩ Pj = Ø,

(C3) ∪ Pi = X,

Then P is a partition of X and the Pi are the blocks of the partition P.

Let now P(X) be the set of partitions on a nonempty finite set X. We may define on P(X) a partial order relation ≤ (reflexive, antisymmetric and transitive) such that P(X), ≤) is a lattice in the sense of Birkhoff (1967), that is, a partial order where every pair of elements has the same least upper bound and the same greatest lower bound. Then, one can prove that all the chains (all the linearly ordered sequences of partitions) of this lattice are equivalent to hierarchical classifications. So, the set C(X) of all these chains is exactly the set of all hierarchical classifications on a set. This set C(X) has itself a mathematical structure: it is a semilattice for set intersection. This model allows us to get all the possible partitions of P(X) and all the possible chains of C(X) (See Figure 4).

Figure 4: The lattice of partitions of a 4-element set.

A first problem is that such partitions are very numerous. For |X| = 9, for example, there is already 21147 partitions. So, when we want to classify some domain of objects (plants, animals, books, and so forth), it is not very easy to examine what classification is the best one among, say, several thousands of them.

A second problem is that the world is not made of chains of partitions. If it were, of course, the game would be over. Everything could be inserted in some hierarchical classification. But, the real world has no reason to present itself as a hierarchical classification. In the real world, we have generally to deal with quite chaotic entities, complicated fuzzy classes and poor structured objects, all that form what we can call ‘rough data’. So when we want to get a clear order, we have to construct it, such that it is extracted from the complicated data. For that, we have to compare objects, to know the degree to which they are similar, and to do so, we need of course a notion of ‘similarity’. In order to make empirical classifications we must evaluate the similarities or dissimilarities between elements to be classified. In the history of taxonomic science, Buffon (1749) and Adanson (1757) have tried to understand the meaning of this evaluation in the following way. First, they claim, we have to measure the distance between the objects by the means of some index, so that we can build classes. Afterwards, we have to measure the distance between classes themselves, so that we can group some classes into classes of classes, and so replace the initial set of objects with an ordered set of classes that is less numerous than them.

What old taxonomists were doing, only basis of observation, can now be carried out with the help of mathematics, using a modern notion of distance. Lerman (1970) and Benzécri (1973) showed that a hierarchical classification, that is, a chain of partitions, is nothing but a particular kind of distance or, a particular kind of dissimilarity (Van Cutsem 1994). It is an ultrametric distance, which gives tree representations (Barthélemy and Guénoche 1988) and also has the special property to correspond exactly with the chain, so that, when considering all the chains, the set of their corresponding distance matrices makes a semiring (R, +, ×) when we interpret the lattice operations min and max in an anusual but clever manner (+ for min, × for max) (Gondran 1976). Problems arise when the distance between the objects classified is not ultrametric. In such cases, we have to choose the closest ultrametric smaller than the given distance, and so, access to the best hierarchical classification we can get and which is the closest one to the data. However, this kind of approach leads, in general, to relatively unstable classifications.

Indeed, there are two kinds of instability for classifications. The first, Intrinsic instability,,is associated to the plurality of methods (distances, algorithms and so forth) that can be used to make the classifications of objects. The second is extrinsic instability, which is connected to the fact that our knowledge is changing with time, so the definitions of objects (or attributes of the objects) are evolving.

An answer to the question of intrinsic instability is a theorem of Lerman (1970) which says that if the number of attributes (or properties) possessed by the objects of a set X is constant, the associated quasi-order given by any natural metric is the same. But this result has two limits. First, when the sample variance of the number of attributes is a big one, of course, the stability is lost and second, if we classify the attributes, instead of classifying the objects, the reverse is not true.

For extrinsic instability the answers are more difficult to find. We may appeal to methods used in library decimal classifications (UDC, Dewey, and so forth), which make possible infinite ramified extensions, but these classifications, as we have seen, are apt to assume that higher levels are invariant and have also the disadvantage to be enumerative and to degenerate rapidly into simple lists. Also, pseudo-complemented structures (Hilman 1964) that admit some kinds of waiting boxes (or compartments) for indexing things that are not yet classified. We get as well structures whose transformations obey certain rules that have been fixed in advance. That is the case of Hopcroft 3-2 trees (Aho, Hopcroft, Ulmann 1983) for instance, or of structures close to these ones (Larson and Walden, 1979). In recent years, new models for making classifications came from conceptual formal analysis (Barwise and Seligman, 2003), computer science or views using non-classical logics in the domain of formal ontologies (Smith 1997, 2003). In computer science, for example, the concept of Abstract Data Type (ADT), related to the concept of Data Abstraction, important in object-oriented programming, may be viewed as a generalization of mathematical structures. An ADT is a mathematical model for data types, where a data type is defined by its behavior from the point of view of a user of the data. More formally, an ADT may be defined as a “class of objects whose logical behavior is defined by a set of values and a set of operations” (Dale-Walker 1996), which is strictly analogous to algebraic structures in mathematics. So, if we are not satisfied by a rough classification like the partition into collections, streams and iterators (support loops accessing data items) and relational data structures that capture relationships between data items, we must admit that ADT can also be regarded as a generalized approach of a number of algebraic structures, such as lattices, groups, and rings (Lidi 2004). Hence, classifications of ADT turn into classifications in algebraic specifications of ADT (Veglioni 1996). In this context, computer science adds nothing to mathematics and the problem is now that a classification of mathematical structures using, for instance, Category theory, as Pierce (1970) tried does not bring a sufficient answer because a category may exist while its objects are not necessarily constructible (Parrochia-Neuville 2013).

So, none of the previous approaches is very convincing for solving the basic problem, which always remains the same. We are lacking a general theory of classifications, which would only be able to study and, in the best case, solve some the main problems of classification.

b. A Glance at an Intensional Approach

Instead of making partitions by dividing a set of entities, so that the classes obtained in this way are extensional classes, as we saw in the previous section, we can instead proceed by associating a description to a set of entities. In this case, the classes are called intensional classes. Aristotle himself mixed the two points of view in his logic but Leibniz was the first to propose a purely intensional interpretation of classes. For a long time, that view was a minority and has never won unanimous support among the Ancient philosophers and logicians (as the numerous discussions between Aristotle and Plato, Ramus and Pascal, Jevons and Joseph demonstrate). However, the development of computer science brought this view back, since for declarative languages and particularly object-oriented languages, pure extensional classes or sets are rather uncommon. In this approach, the intension can be given either a priori, for example by a human actor from his knowledge of the domain, or a posteriori, when it is deduced from the analysis of a set of objects. In object-oriented modeling and programming, classes are traditionally defined a priori, with their extension mostly derived at running stage. This is usually done manually (intension being represented by logical predicates or tags), but techniques for a posteriori class discovery and organization also exist. In the context of programming languages, they deal with local class hierarchy modification by adding interclasses and use similarity-based clustering techniques or the Galois lattice approach (Wille 1996).

When there is an unrelated collection of sets, which is the case in artifact-based software classification, an issue is to compare and organize these sets simply by inclusion, or to apply conceptual clustering techniques. However, most of objected oriented languages are concerned with hierarchies, whose structure may be a tree, a lattice, or any partial order. The reason is that such structures reflect the variety of languages, some of them admitting multiple inheritance (C++, Eiffel), others only single inheritance (Smalltalk). Java has a special policy concerning this point: it admits two kinds of concepts, classes and interfaces, with single inheritance for classes and multiple inheritance for interfaces.

The viewpoint of Aristotle was the following: the division must be exhaustive, with parts mutually exclusive, and an indirect consequence of Aristotle’s principles is that only leaves of the hierarchy should have instances. Furthermore, the divisions must be based on a common concern whose modern name is the ‘discriminator’ in Unified Modeling Language (UML). But usual programming practices do not necessarily satisfy those principles. Multiple inheritance, for example, is contradictory with the assumption of mutually exclusive parts, and instances may in general be directly created from all (non-abstract) classes. Direct subclasses of a class can be derived according to different needs with different discriminators, but there is no evidence that this approach leads to relevant classifications. Objected oriented approaches, which transgress Aristotelian principles, are almost always practical storage modes but do not satisfy the main requisites of good classifications.

There are main principles that yield good classification, which are described in the intensional perspective. First–with Apostel [1963]– are some basic definitions.

From an intensional viewpoint, a division (or partition) is a closed formula F, which contains some assertion of the type (P ⊃ (Q1 ∨ Q2 ∨…∨ Qn)). So, a classification is a sequence of implicative-disjunctive propositions which takes the following form: everything which has the property P has also one of the n properties Q1 … Qn. Everything which has the property Qr has also the property S, and so on (Apostel 1963, 188).

A division is essential if the individuals having the property P – and only this individual – may also have one of the properties Qi. So, we can see that there are degrees in essentiality insofar as the number of individuals having the Q’s without having the P’s is greater or less. At every level, a classification may be probably or necessarily essential or exhaustive, or exclusive.

We call intensional weight w(P) of a property P, the set of disjunctions implied by this property (with necessity, factuality or probability). Properties defining classes in the same level may have extremely variable intensional weights. The basis of a division is the constant relation R, if any, between the properties of two different classes of this division.

A basis of division is (partially or totally) exhausted in some level insofar as, for this level, we do not find, in any case, true disjunctive propositions that are implied by the properties of this level and whose terms are connected by this very relation R.

A division is said to follow another one immediately (or to be immediately subsequent) if, for all P properties of the first, and for all Q properties of the second that are disjunctively implied by the P’s, there exists no sequence of R properties disjunctively implied by the P’s and disjunctively implying the Q’s.

The form of a property defining a class is the logical form of this property (conjunction of properties, disjunction of properties, negation of properties, single property).

For Apostel, an optimal classification should satisfy the following requisites:

Every level needs a basis for division;

No new basis for division shall be introduced before the previous one is exhausted;

Every division is essential;

Intensional weights of classes in a given level are comparable and relations between intensional weights of subsequent division properties in the classification must be constant.

Properties used to define classes are conjunctive ones, and not negative ones.

From the intensional viewpoint, divisions must be immediately subsequent.

In real domains, these requirements, or some of them, fail to hold. Levels are often extensionally equivalent but intensionally, the basis of division, the intensional weight, and so forth may change or not.

A natural classification is such that the definition of the domain classified determines in one and the same way the choice of the criteria of classification. It means that the fundamental set may be divided such that the division in the first level of the classification is an essential and subsequent one.

Intensional and extensional classifications are intimately related. Gathering entities in sets to produce extensional classes implies tagging these entities by their membership to these classes. But, intensional classes, built according to these descriptions, have an extension, which may be different from the initial extensional classes. So, in fact, both perspectives are not totally isomorphic and from Peirce (Hulwitt 1997) to Quine (1969), and presently, the question of natural classes remains an open and somewhat controversial question.

6. The Idea of a General Theory of Classifications

The idea of a general theory of classiﬁcations is not new. Such a project has been anticipated by Kant’s logic at the end of the 18th century. Then it was followed by many attempts to classify sciences at the beginning of the 19th century (Kedrov 1977) and had been posed by Auguste Comte in his Cours de philosophie positive (Comte 1975) as a general theory based on the study of symmetries in nature. Comte was inspired by mathematician Gaspard Monge and his classification of surfaces in geometry. However, this remains, in the work of Comte, a wishful thought. In the same way, the French naturalist Augustin-Pyramus de Candolle, published in 1813 an Elementary Theory of Botany, a book in which he introduced the term ‘taxonomia’, used in this work for the ﬁrst time (de Candolle 1813). De Candolle showed that Botany had to leave artiﬁcial methods for natural ones, in order to get a method independent from the nature of the objects. Unfortunately, nothing very concrete or precise followed his remarks. Moreover, the previous projects were only concerned with ﬁnite classiﬁcations, particularly, biological ones. A higher and more general view came into light around the 1960s with the Belgian logician Leo Apostel. Apostel (1963) wanted to write a concrete version of Set theory, and, in order to do that, needed axioms that allow him to include in the theory only the classes actually existing in the world. As such, Apostel was led to ask some questions about the well-known axioms of Zermelo-Fraenkel’s Set theory. He did not reject the whole ZF-axiomatics but however suspected axioms like the pairing axiom, the axiom of separation and the power set axiom. He also left optional the axiom of infinity and had rather a negative opinion about the axiom of choice. This project got a new revival with the recent book of Parrochia-Neuville (2013).

The hardships of solving the problem of instability of classifications provided motivation for a search for some clear composition laws to be defined on the set of classifications over a set and to a true algebra of classifications, if possible, which is very difficult because this algebra would have to be, in principle, commutative and non-associative. This search is all the more crucial that a recent theorem proved by Kleinberg (2002) shows that one cannot hope to find a classifying function which would be together scale invariant, rich enough and consistent. This result means that we cannot find empirical stable classifications by using traditional clustering methods.

In the past, some attempts have been made to formalize non-commutative parenthesized products: Comtet (1970) and Neuville, in the 1980s used the Lukasiewicz’s Reverse Polish Notation (RPN), named also Postfix Notation, whose advantage is not only to make brackets or parentheses superfluous, but also to perform calculations on trees in the required order. But, a general algebra of classifications on a set is not known, even if some new models−Loday’s dendriform algebras, for example, which work very well for trees (See Dzhumadil’daev-Löfwall 2002)−are good candidates. In any event, we are invited to look for it, for two reasons. First, the world is not completely chaotic and our knowledge is evolving according to some laws. Second, there exist quasi-invariant classifications in physics (elementary particle classification), chemistry (Mendeleyev table of Elements), crystallography (the 232 groups of crystallographic structures) among others. Most of these good classifications are based on some mathematical structures (Lie groups, discrete groups, and so forth.). To address questions concerning classification theory, and clarify the different domains of it, one may propose this final view (See Figure 6):

When our mathematical tools apply only to sense data, we get phenomenal classifications (by clustering methods): these are generally quite unstable.

When our mathematical tools deal with crystallographic or quantum structures, we get what we call, using a Kantian concept, noumenal classifications (for instance, by invariance of discrete groups or Lie Groups). These are generally more stables.

When we search a general theory of classifications (including infinite ones), we are in the domain of pure mathematics. In this field, ordering and articulating the infinite set of classifications comes to construct the continuum.

Figure 6: Metaclassification

This problem is far from being solved because there are a lot of unstable theories (Shelah 1978, 1998). However, the recent work of Parrochia-Neuville (2013) assumes the conjecture that a metaclassification, that is, a classification of all mathematical schemes of classifications, does exist. The reason is that all these forms may be expressed as ellipsoids of an n-dimensional space (Jambu 1983) that must converge necessarily on a point, the index of the classification. If the real proof comes, this will give a theorem of existence of such a structure from which a number of important results could follow.

7. References and Further Readings

Adanson, M. 1757. Histoire naturelle du Sénégal. Paris: Claude-Jean-Baptiste Bauche.

Aho, A.V., Hopcroft, J.E, Ulmann, J.D. 1983. Data Structures and algorithms. Reading (Mass.): Addison-Wesley Publishing Company.

Agassiz, L. 1962. Essay on Classification (1857), reprint. Cambridge: Harvard University Press.

Apostel, L. 1963. Le problème formel des classifications empiriques. La Classification dans les Sciences. Gembloux: Duculot.

Aristotle, 1984. The Complete Works. Princeton: Princeton University Press.

Barbut M., Monjardet, B. 1970. Ordre et classifications, 2 vol. Paris: Hachette.

Barthélemy, J.-P., A. Guénoche. 1988. Les arbres et les représentations des proximités. Paris: Masson.

Barwise, J., Seligman, J. 2003. The logic of distributed systems. Cambridge: Cambridge University Press.

Béthery, A. 1982. Abrégé de la classification décimale de Dewey. Paris: Cercle de la librairie.

Bliss, H. E. 1929. The organization of knowledge and the system of the sciences. New York: H. Holt and Company.

Benzécri, J.-P., et alii. 1973. L’analyse des données, 1, La taxinomie, 2 Correspondances. Paris: Dunod.

Birkhoff, G. 1935. On the structure of abstract algebras. Proc. Camb. Philos. Soc. 31, 433-454.

Birkhoff, G. 1967. Lattice theory (1940), 3rd ed. Providence: A.M.S.

Brucker F., Barthélemy, J.-P. 2007. Eléments de Classification, aspects combinatoires et algorithmiques. Paris: Hermès-Lavoisier.

Buffon, G. L. Leclerc de, 1749. Histoire naturelle générale et particulière (vol. 1). Paris: Imprimerie royale.

Candolle (de), A. P. 1813. Théorie élémentaire de la Botanique ou exposition des principes de la classification naturelle et de l’art d’écrire et d’étudier les végétaux, first edition. Paris: Deterville.

Comte, A. 1975. Philosophie Première, Cours de Philosophie Positive (1830), Leçons 1-45. Paris: Hermann.

Comtet, L. 1970. Analyse combinatoire. Paris: P.U.F..

Dagognet, F. 2002. Tableaux et Langages de la Chimie (1967). Seyssel: Champ Vallon.

Dagognet, F. 1970. Le Catalogue de la Vie. Paris: P.U.F..

Dagognet, F. 1984. Le Nombre et le lieu. Paris: Vrin.

Dagognet, F. 1990. Corps réfléchis. Paris: Odile Jacob.

Dahlberg, I., 1976. Classification theory, yesterday and today. International Classification 3 n°2, pp. 85-90.

Dale, N., Walker, H. M. 1996. Abstract Data Types: Specifications, Implementations, and Applications. Lexington, Massachusetts: D.C. Heath and Company.

Darwin, C.R., 1964. On the Origin of Species (1859), reprint. Cambridge: Harvard University Press.

De Grolier, E. 1962. Etude sur les catégories générales applicables aux classifications documentaires, Unesco.

Dobrowolski, Z. 1964. Etude sur la construction des systèmes de classification. Paris, Gauthier-Villars.

Dubreil, P., Jacotin, M.-L. 1939. Théorie algébrique des relations d’équivalence. J. Math. 18, pp. 63-95.

Dzhumadil’daev,A. et Löfwall, C. 2002. Trees, free right-symmetric algebras, free Novikov Algebras and Identities. Homology, homotopy and Applications, vol.(4(2), pp. 165-190.

Foucault, M. 1967. Les Mots et les Choses. Paris: Gallimard.

Gondran, M. 1976. La structure algébrique des classifications hiérarchiques. Annales de l’Insee, pp. 22-23.

Granger, G.-G. 1980. Pensée formelle et Science de l’Homme (1967). Paris: Aubier-Montaigne.

Hilman, D.J. 1965. Mathematical classification technics for non static document collections, with particular reference to the problem of revelance. Classification Research, Elsinore Conference Proceedings, Munksgaard, Copenhagen, pp. 177-209.

Huchard, M., R. Godin, , A. Napoli, A. 2003. Objects and Classification. ECOOP 2000 Workshop reader, J. Malenfant, S. Moisan, A. Moreira (Eds), LNCS 1964. Berlin-Heidelberg-New York: Springer-Verlag, pp 123-137.

Hulswit, M. 1997. Peirce’s Teleological Approach to Natural Classes. Transactions of the Charles S. Peirce Society, pp. 722-772.

Jambu, M. 1983. Classification automatique pour l’analyse des données, 2 vol.. Paris: Dunod.

Jardine N., Sibson, R. 1971. Numerical Taxonomy. New York: Wiley.

Joly, R. 1956. Le thème philosophique des genres de vie dans l’Antiquité grecque. Bruxelles: Mémoires de l’Académie royale de Belgique, classe des Lettres et des Sciences mor. et pol., tome Ll, fasc. 3.

Kant, E. 1988. Logic. New York: Dover Publications.

Kedrov, B. 1977. La Classification des Sciences (vol. 2). Moscou: Editions du Progrès.

Kleinberg, J. 2002. An impossibility theorem for Clustering. Advances in Neural Information Processing Systems (NIPS), 15, pp. 463-470.

Krastner M. 1953-1954. Espaces ultramétriques et ultramatroïdes. Paris: Séminaire, Faculté des Sciences de Paris.

Larson, J.A., Walden, W.E. 1979. Comparing insertion shemes used to update 3-2 trees. Information Systems, vol.4, pp. 127-136.

Lerman, I.C. 1970. Les bases de la classification automatique. Paris: Gauthier-Villars.

Lerman, I.C. 1981. Classification et analyse ordinale des données. Paris: Dunod.

Lidi R., 2004. Abstract Algebra. Berlin-Heidelberg-New York: Springer-Verlag.

Luszczewska-Romahnowa S., Batog T. 1965a. A generalized classification theory I. Stud. Log., tom XVI, pp. 53-70.

Luszczewska-Romahnowa S., Batog T. 1965b. A generalized classification theory II. Stud. Log., tom XVII, pp. 7-30.

MacNeille 1937. Partially ordered sets. Transaction Amer. Math. Soc., vol. 42, pp. 416-460.

Ore O. 1942. Theory of equivalence relations. Duke Math. J. 9, pp. 573-627.

Ore O. 1943. Some studies on closer relations. Duke Math. J. 10, pp. 761-785.

Parrochia, D., Neuville, P. 2013. Towards a general theory of classifications. Bäsel: Birkhaüser.

Peirce C. S. 1880. On the Algebra of Logic. American Journal of Mathematics 3, pp. 15-57.

Pierce, R.S. 1970. Classification problems. Mathematical System theory, vol. 4, n°1, March, pp. 65-80.

Plato, 1997. The Complete Works. Cambridge: Hacking publishing Company

Porphyry, 2014. On Aristotle’s Categories. London, New York: Bloomsbury Publishing Plc.

Quine, W.V.O. 1969. Ontological Relativity and Other Essays. New York: Columbia University Press.

Ranganathan, S. R. 1933. Colon Classification. Madras: Madras Library Association.

Ranganathan, S. R. 2006. Prolegomena to Library Classification (1937), Reprint. New Delhi: Ess Pub..

Rasiowa H., Sikorski, R. 1970. The Mathematics of Metamathematics. Cracovia: Drukarnia Uniwersytetu Jagiellonskiego.

Riordan, J. 1958. Introduction to combinatorial analysis. New York: Wiley.

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Shelah, S. 1988. Classification Theory (1978). Amsterdam: North Holland.

Shröder, E. 1890. Vier Kombinatorische Probleme. Z. Math. Phys. 15, pp. 361-376.

Smith, B. 1997. Boundaries: An Essay in Mereotopology. L. Hahn (ed.), The Philosophy of Roderick Chisholm. La Salle, Open Court: Library of Living Philosophers, pp. 534-561.

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Sokal R. R., Sneath, P.H. 1963. Principle of numerical taxonomy. San Francisco: W. H. Freeman.

Sokal, R. R., and Sneath, P. H. 1973. Numerical Taxonomy, the principles and practice of numerical classifications. San Francisco: W. H. Freeman.

Van Cutsem B. (ed.) 1994. Classification and dissimilarity analysis. New York-Berlin-Heidelberg: Springer Verlag.

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Windsor, M. P. 2009. Taxonomy was the foundation of Darwin’s evolution. Taxon 58, 1, pp. 43-49.

Wille, R. 1996. Restructuring lattice theory: an approach based on hierarchy of concepts. Rival, I (ed.) Ordered Sets. Boston: Reidel, pp. 445-470.

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Author Information

Daniel Parrochia

Email: daniel.parrochia@wanadoo.fr

Université Jean Moulin – Lyon III

France

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Classification system — Science Learning Hub

Classification system — Science Learning Hub Topics Concepts Citizen science Teacher PLD Glossary Sign in Topics Concepts Citizen science Teacher PLD Glossary Sign in NOTIFICATIONS Article Classification system Resource Glossary Related topics & concepts Add to collection + Create new collection In the 18th century, Carl Linnaeus published a system for classifying living things, which has been developed into the modern classification system. People have always given names to things that they see, including plants and animals, but Linnaeus was the first scientist to develop a hierarchal naming structure that conveyed information both about what the species was (its name) and also its closest relatives. The ability of the Linnean system to convey complex relationships to scientists throughout the world is why it has been so widely adopted. Rights: The University of Waikato Linnean classification system In the 18th century, Carl Linnaeus published a system for classifying living things, which has been developed into the modern classification system. Despite existing for hundreds of years, the science of classification — taxonomy — is far from dead. Classification of many species, old and new, continues to be hotly disputed as scientists find new information or interpret facts in new ways. Arguments are fierce and species do change names, but only after a wealth of information has been gathered to support such a big step. One of the new reasons why species are being re-evaluated is because of DNA analysis. Basic genetic analysis information can change our ideas of how closely two species are related and so their classification can change, but how does the whole system work? Nature of science Improved technologies have altered our understanding of the world. In astronomy, the invention of the telescope enabled astronomers to observe outer space and see what they hadn’t been able to see before, and biologists use the microscope to observe the unseen world. Now, DNA technology has allowed scientists to re-examine the relationships between organisms to refine the classification system. Kingdom When Linnaeus first described his system, he named only two kingdoms – animals and plants. Today, scientists think there are at least five kingdoms – animals, plants, fungi, protists (very simple organisms) and monera (bacteria). Some scientists now support the idea of a sixth kingdom – viruses – but this is being contested and argued around the world. Phylum Below the kingdom is the phylum (plural phyla). Within the animal kingdom, major phyla include chordata (animals with a backbone), arthropoda (includes insects) and mollusca (molluscs such as snails). Phyla have also been developed and reorganised since the original work by Linnaeus – as scientists discover more species, more categories and subcategories are put in place. Class Each phylum is then divided into classes. Classes within the chordata phylum include mammalia (mammals), reptilia (reptiles) and osteichthyes (fish), among others. Order The class will then be subdivided into an order. Within the class mammalia, examples of an order include cetacea (including whales and dolphins), carnivora (carnivores), primates (monkeys, apes and humans) and chiroptera (bats). Family From the order, the organism will be classified into a family. Within the order of primates, families include hominidae (great apes and humans), cercopithecidae (old world monkeys such as baboons) and hylobatidae (gibbons and lesser apes). Genus and species Naming organisms Dr Peter Buchanan and Dr Robert Hoare, of Manaaki Whenua – Landcare Research, introduce the classification system that scientists use to identify and name organisms. Finally, the classification will come to the genus (plural genera) and species. These are the names that are most commonly used to describe an organism. One outstanding feature of the Linnean classification system is that two names are generally sufficient to differentiate from one organism to the next. An example within the primate family is the genus Homo for all human species (for example, Homo sapiens) or Pongo for the genus of orangutan (for example, Pongo abelii for the Sumatran orangutan or Pongo pygmaeus for the Bornean orangutan). Rights: Peter Lakomy, licenced through 123RF Limited Pongo pygmaeus Two names at the genus and species level are generally sufficient to differentiate from one organism to the next, for example, Pongo pygmaeus. Constant evolution While this system of classification has existed for over 300 years, it is constantly evolving. Classification in the 1700s was based entirely on the morphological characteristics (what something looks like) of the organism. Those that looked most alike were put closest together in each category. This can be depicted as a tree, with the diverging branches showing how different the species become as you move out from the kingdoms (trunk). Now, a radical shift in the grouping of organisms is occurring with the development of DNA technologies. Sequencing of the genetic code of an organism reveals a great deal of information about its similarity with and relationship to other organisms, and this classification often goes against the traditional morphological classification. Scientists are debating which species are most closely related and why. Currently in New Zealand, there are projects to sequence kiwi and tuatara DNA that may revolutionise the way we think about these species and their closest living relatives. However, DNA technology is still expensive and time-consuming, so the first step in any classification continues to rely on a comparison of morphological features, similar to the process that Linnaeus undertook in the 1700s. Rights: The University of Waikato Te Whare Wānanga o Waikato Tuatara classification This image represents tuatara classification. It begins with the broadest, most inclusive taxon (group) and moves through subdivisions until it reaches species – the smallest and most exclusive taxon. Activity idea Your students can learn more about how the Linnaean classification system works with this activity, Insect mihi. Students write a formal introduction for an insect species of their choice, including information about the insect’s relationship to other animals and also the land. Find out more Classification is not a field that stays still and this means scientists and taxonomists sometimes have to reassess classifications. Learn more in Leon Perrie's thought provoking blog, Why do scientific names change? Useful links Access the New Zealand Threat Classification System (NZTCS) database here. Learn more about the five kingdoms on the Biology Online website. Tweet Published 30 April 2009, Updated 3 September 2018 Referencing Hub articles Go to full glossary Add 0 items to collection + Create new collection Download 0 items Download all Twitter Pinterest Facebook Instagram Email Us See our newsletters here. News and EventsAboutContact usPrivacyCopyrightHelp Curious Minds is a Government initiative jointly led by the Ministry of Business, Innovation and Employment, the Ministry of Education and the Office of the Prime Minister’s Chief Science Advisor. Science Learning Hub – Pokapū Akoranga Pūtaiao © 2007-2024 The University of Waikato Te Whare Wānanga o Waikato Would you like to take a short survey? This survey will open in a new tab and you can fill it out after your visit to the site. Yes No

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